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Accelerating Convergence of Score-Based Diffusion Models, Provably
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abstract
Score-based diffusion models, while achieving remarkable empirical performance, often suffer from low sampling speed, due to extensive function evaluations needed during the sampling phase. Despite a flurry of recent activities towards speeding up diffusion generative modeling in practice, theoretical underpinnings for acceleration techniques remain severely limited. In this paper, we design novel training-free algorithms to accelerate popular deterministic (i.e., DDIM) and stochastic (i.e., DDPM) samplers. Our accelerated deterministic sampler converges at a rate $O(1/{T}^2)$ with $T$ the number of steps, improving upon the $O(1/T)$ rate for the DDIM sampler; and our accelerated stochastic sampler converges at a rate $O(1/T)$, outperforming the rate $O(1/\sqrt{T})$ for the DDPM sampler. The design of our algorithms leverages insights from higher-order approximation, and shares similar intuitions as popular high-order ODE solvers like the DPM-Solver-2. Our theory accommodates $\ell_2$-accurate score estimates, and does not require log-concavity or smoothness on the target distribution.
Forward citations
Cited by 6 Pith papers
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Faster Diffusion Models via Higher-Order Approximation
A new higher-order ODE sampler for diffusion models is proven to reach ε total-variation accuracy with eO(d^{1+2/K}/ε^{1/K}) iterations under mild assumptions.
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Provable Diffusion Posterior Sampling for Bayesian Inversion
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Likelihood Matching for Diffusion Models
Likelihood Matching trains diffusion models by maximizing a Gaussian quasi-likelihood of reverse transitions driven by score and Hessian estimates, with consistency and total-variation convergence guarantees.
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Fast Convergence for High-Order ODE Solvers in Diffusion Probabilistic Models
A TV convergence bound O(d^{7/4} ε^{1/2} + d(dH)^p) is proved for p-th order (exponential) Runge-Kutta samplers of probability-flow ODEs under C² smoothness of the learned score.
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Solving Inverse Problems via Diffusion-Based Priors: An Approximation-Free Ensemble Sampling Approach
A weighted-particle sampler evolves the posterior through the diffusion model's reverse dynamics, with theoretical error bounds and improved image reconstructions.
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Non-asymptotic convergence bound of conditional diffusion models
CARD's generated conditional distribution is shown to converge in Wasserstein distance to the true conditional distribution, with a separate score-estimation error bound controlled by network resolution and distributi...
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